Dielectric Microcavity Research Articles

Lasing modes in a spiral-shaped dielectric microcavity

The resonance patterns and lasing modes in a spiral-shaped dielectric microcavity are investigated through passive and active medium calculations. We find that the high-Q resonance modes are whispering-gallery-like modes, and these resonance modes can be easily excited as lasing modes. We also find that the quasi-scarred resonance mode, which shows strong directional emission beams from the cavity boundary, can be excited with selectively applied external pumping. Through a spectral analysis of the time evolution of the light field, the competition between these lasing modes is discussed.

Plasmonic field enhancement and SERS in the effective mode volume picture

The controlled creation of nanometric electromagnetic field confinement via surface plasmon polariton excitations in metal/insulator/metal heterostructures is described via the concept of an effective electromagnetic mode volume Veff. Extensively used for the description of dielectric microcavities, its extension to plasmonics provides a convenient figure of merit and allows comparisons with dielectric counterparts. Using a one-dimensional analytical model and three-dimensional finite-difference time-domain simulations, it is shown that plasmonic cavities with nanometric dielectric gaps indeed allow for physical as well as effective mode volumes well below the diffraction limit in the gap material, despite significant energy penetration into the metal. In this picture, matter-plasmon interactions can be quantified in terms of quality factor Q and Veff, enabling a resonant cavity description of surface enhanced Raman scattering.

Polarization properties and dispersion relations for spiral resonances of a dielectric rod

Dielectric microcavities based on cylindrical and deformed cylindrical shapes have been employed as resonators for microlasers. Such systems support spiral resonances with finite momentum along the cylinder axis. For such modes the boundary conditions do not separate and simple TM and TE polarization states do not exist. We formulate a theory for the dispersion relations and polarization properties of such resonances for an infinite dielectric rod of arbitrary cross-section and then solve for these quantities for the case of a circular cross-section (cylinder). Useful analytic formulas are obtained using the eikonal (Einstein-Brillouin-Keller) method which are shown to be excellent approximations to the exact results from the wave equation. The major finding is that the polarization of the radiation emitted into the far-field is linear up to a polarization critical angle (PCA) at which it changes to elliptical. The PCA always lies between the Brewster and total-internal-reflection angles for the dielectric, as is shown by an analysis based on the Jones matrices of the spiraling rays.

Analysis of high-quality modes in open chaotic microcavities

We present a numerical study of the high-quality modes in two-dimensional dielectric stadium microcavities. Although the classical ray mechanics is fully chaotic in a stadium billiard, all of the high-quality modes show a ``strong scar'' around unstable periodic orbits. When the deformation (ratio of the length of the straight segments over the diameter of the half circles) is small, the high-quality modes correspond to whispering-gallery-type trajectories and their quality factors decrease monotonically with increasing deformation. At large deformation, each high-quality mode is associated with multiple unstable periodic orbits. Its quality factor changes nonmonotonically with the deformation, and there exists an optimal deformation for each mode at which its quality factor reaches a local maximum. This unusual behavior is attributed to the interference of waves propagating along different constituent orbits that could minimize light leakage out of the cavity.

Planar cavity modes in void channel polymer photonic crystals

Planar dielectric microcavities embedded in woodpile void channel photonic crystals with stop bands in the stacking direction ranging from 4.3 to 4.8 microm in wavelength were generated by femtosecond-laser direct writing in a solid polymer. Infrared transmission spectra revealed fundamental and second-order modes crossing the stop gap region with a free spectral range of 430 nm on varying the microcavity size from 0.3 to 2.25 microm. Supercell calculations confirmed the cavity size dependence of highly localized cavity modes, whereas the angle of incidence was accounted for using a simple Fabry-Perot model.

Quasiscarred Resonances in a Spiral-Shaped Microcavity

We study resonance patterns of a spiral-shaped dielectric microcavity with chaotic ray dynamics. Many resonance patterns of this microcavity, with refractive indices n=2 and 3, exhibit strong localization of simple geometric shape, and we call them quasiscarred resonances in the sense that there is, unlike conventional scarring, no underlying periodic orbits. It is shown that the formation of a quasiscarred pattern can be understood in terms of ray dynamical probability distributions and wave properties like uncertainty and interference.

Mathematical study of the two-dimensional lasing problem for the whispering-gallery modes in a circular dielectric microcavity

Microdisk lasers are investigated for their thresholds characteristics. We present a novel approach for studying the threshold gains of the whispering-gallery (WG) and other modes based on solving the boundary value problem for the Maxwell's equations. The novelty is that we consider the real-value pairs of frequencies and material gains as eigenvalues. In the two-dimensional (2D) approximation this problem is reduced to the set of independent transcendental equations. A Newton's method is further used to calculate the thresholds and natural frequencies numerically.

On cavity modification of stimulated Raman scattering

We study theoretically stimulated Raman scattering (SRS) in a nonlinear dielectric microcavity and compare SRS thresholds for the cavity and the bulk material it is made of. We show that cavity SRS enhancement results solely from the intensity build up in the cavity and from the differences of the SRS dynamics in free and confined space. There is no significant modification of the Raman gain due to cavity QED effects. We show that the SRS threshold depends significantly on the nature of the dominating cavity decay as well as on the coupling technique with the cavity used for SRS measurements.

Resonant-cavity Schottky photodetectors with a grating profiled surface

Modeling of the optical response and quantum efficiency (QE) of a photodetector having a metal clad dielectric microcavity with periodic texturing of the top-metal electrode is examined at an optical communication wavelength (λ=1.3μm). It is shown that microstructuring the top-metal layer allows coupling to surface plasmons and leads to practically zero top reflectivity near normal incidence. This is significantly lower than that of a planar counterpart structure the top reflectivity of which is in excess of 90%. The calculated efficiency using a Monte Carlo method is compared with that obtained analytically to demonstrate the effect of elastic and inelastic carrier scattering on the overall yield. The variations of both the efficiency and the bandwidth as a function of the active layer thickness suggests that the increase in the QE when increasing the active layer width is much less important compared to the very pronounced decrease in the bandwidth.

Energy relaxation by polariton emission in asymmetric planar multilayer microcavities

The effects of a thin metallic layer on the electromagnetic properties of an asymmetric planar dielectric microcavity are explored and their influence on the emission characteristics and cooperative effects are determined for dipole emitters localised in the vicinity of the metallic layer. We report novel effects arising from the variation of the electron density of the metal and there are unusual features due to pair cooperative effects arising from the dielectric mismatch.

Boundary element method for resonances in dielectric microcavities

A boundary element method based on a Green's function technique is introduced to compute resonances with intermediate lifetimes in quasi-two-dimensional dielectric cavities. It can be applied to single or several optical resonators of arbitrary shape, including corners, for both TM and TE polarization. For cavities with symmetries a symmetry reduction is described. The existence of spurious solutions is discussed. The efficiency of the method is demonstrated by calculating resonances in two coupled hexagonal cavities.

Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities

The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced ???chaotic??? modes for the generic case. The wavevector quantization rule for the quasi-bound modes is derived and given a simple physical interpretation in terms of Fresnel reflection; quasi-bound modes are explictly constructed and compared to numerical results. The effect of discrete symmetries of the resonator is analyzed and shown to give rise to quasi-degenerate multiplets; the average splitting of these multiplets is calculated by methods from quantum chaos theory.

Spontaneous emission in microcavity electrodynamics

We present a general, semimicroscopic, self-consistent treatment of spontaneous emission for a two-level atom in a dielectric microcavity with arbitrary shape. Both lossless and absorbing media are considered. Our approach is based on linear-response theory and the coupled-dipole method. We illustrate our method on spherical and cubic cavities. We discuss the Purcell effect, the frequency shift, the local-field effect, and the dipole-dipole coupling experienced by a source placed in a microcavity.

Analytical calculation of the extraction efficiency of microcavity light-emitting diodes for display and fiber coupling applications

This paper presents a simple analytical expression of the extraction efficiency for planar dielectric microcavity light-emitting diodes (MCLEDs) based on two distributed Bragg reflectors (DBRs). The calculations take into account the optical properties of the resonator (reflectivities and index contrast of the DBRs, cavity length, refractive index of the outside medium), as well as the spectral properties of the active material. The analytical results are compared to exact numerical calculations based on the plane wave expansion method and show good agreement. Simple design rules for optimizing the extraction efficiency of MCLEDs are proposed and discussed for display and fiber coupling applications. The limits of MCLEDs are finally investigated and compared to those of conventional light-emitting diodes.

Deviation from Snell’s law for beams transmitted near the critical angle: application to microcavity lasers

We show that when a narrow beam is incident upon a dielectric interface near the critical angle for total internal reflection it will be transmitted into the far field with an angular deflection from the direction predicted by Snell's law, because of a phenomenon that we call "Fresnel filtering." This effect can be quite large for the parameter range that is relevant to dielectric microcavity lasers.

Ballistic trajectories of optical wave packets within microcavities

We present time-resolved measurements of the ballistic trajectory of ultrashort optical wave packets circulating near the surface of a dielectric microcavity. The wave-packet dynamics are determined by using two-color two-photon induced fluorescence of Coumarin 510 within the microcavity as a correlator. Ballistic motion of the wave packets in whispering gallery modes and rainbow trajectories has been deduced from the time delay between collisions of the two wave packets. The cavity ringdown time is measured for each of the wave packets, which retain their integrity even after several round trips.

Planar dielectric microcavity light-emitting diodes: Analytical analysis of the extraction efficiency

This article presents a simple analytical expression for the extraction efficiency of planar dielectric microcavity light-emitting diodes (MCLEDs) based on two distributed Bragg reflectors (DBRs). The calculations take into account the optical properties of the resonator (reflectivities and index contrast of the DBRs, cavity length, refractive index of the outside medium), as well as the spectral properties of the active material. The impact of these factors on the extraction efficiency is investigated and compared to the results of exact numerical calculations. Simple design rules for optimizing the extraction efficiency of MCLEDs are derived and discussed for display and fiber coupling applications.

Microtorus: a high-finesse microcavity with whispering-gallery modes

We demonstrate a 165-mu;m oblate spheroidal microcavity with a free spectral range of 383.7 GHz (3.06 nm), a resonance bandwidth of 23 MHz (quality factor Q approximately 10(7)) at 1550 nm, and finesse F>/=10(4) . The highly oblate spheroidal dielectric microcavity combines a very high Q factor, typical of microspheres, with a vastly reduced number of excited whispering-gallery modes (by 2 orders of magnitude). The very large free spectral range in this novel microcavity-a few hundred gigahertz instead of a few gigahertz as in typical microspheres-is desirable for applications in spectral analysis, narrow-linewidth optical and rf oscillators, and cavity QED.

Observation of emission from chaotic lasing modes in deformed microspheres: displacement by the stable-orbit modes

By combining detailed imaging measurements at different tilt angles with simulations of ray emission from prolate-deformed lasing microdroplets, we conclude that the dominant contribution to the laser emission of such three-dimensional dielectric microcavities must come from modes associated with the chaotic region of the ray phase space. As a particularly striking signature, maximum emission from such chaotic lasing modes is not from tangent rays emerging from the highest curvature part of the rim. The laser emission is observed and calculated to be nontangent and displaced from the highest curvature regions owing to the presence of stable orbits. In this paper we present the first experimental evidence for this phenomenon of dynamical eclipsing.

Enhanced backward-directed multiphoton-excited fluorescence from dielectric microcavities

We demonstrate theoretically and experimentally that one-, two-, and three-photon excited fluorescence from dye molecules in spherical microcavities has an asymmetrical angular distribution and is enhanced in the backward direction. The enhancement ratios (of intensities at 180 degrees and 90 degrees ) are 9, 5, and 1.8 for three-, two-, and one-photon excitation, respectively. Even larger ratios are expected for microspheres with an index of refraction larger than that used in the experiments. Because of the reciprocity principle and concentration of the incident wave inside particles, the backward enhancement is expected to occur even with nonspherical particles.